Suppose you want to cut 20 identical boards of length 5 feet

Suppose you want to cut 20 identical boards of length 5 feet. The procedure is to measure and cut the first board then use the first board to measure and cut the second board, then use the second board to measure and cut the third board and so on.

What are the possible lengths of the 20th board, if each time you cut a board, there is a maximum errror of +^{1/4 inch?}

^{The board could be as short as ____ inches or as long as ____inches.}

^{Please round the answer to the nearest hundreth as needed.}

Solution

Length of first board is 5 feet

a =5 and error d = 1/4 or 0.25

If each one is short/long by 0.25 inch, the final board would be 4.75 inches short/long.

Length of 20th board is a +19d = 5 + 19 * 1/4 = 5 +4.75 = 9.75 or 5-4.75 = 0.25